A375093 Numbers for which the number of squares in their Collatz trajectory sets a new record.

1, 3, 9, 27, 133, 315, 747, 2799, 14175, 287061, 530079, 3061987, 18371925, 73487701, 195967203, 1175803221

Offset

1,2

Links

Table of n, a(n) for n=1..16.

Example

a(1) = 1: the square 1 contained in every trajectory at the end,
a(2) = 3: 3 squares in 3 -> 10 -> 5 -> 4^2 -> 8 -> 2^2 -> 2 -> 1^2,
a(3) = 9: 4 squares in 3^2 -> 28 -> ... -> 10 -> as above,
a(4) = 27: the famous long trajectory A008884 includes the 5 squares 22^2, 11^2, 4^2, 2^2, 1^2,
a(5) = 133: 6 squares in 133 -> 20^2 -> 200 -> 10^2 -> 50 -> 5^2 -> ... -> 4^2, 2^2, 1^2,
a(6) = 315: 7 squares in 315 -> 946 -> ... -> 533 -> 40^2 -> 800 -> 20^2 -> as above,
a(7) = 747: 9 squares in 747 -> 2242 -> 1121 -> 58^2 -> 1682 -> 29^2 -> ... -> 1066 -> 533 -> as above.

Prog

(PARI) nextc(x) = if (x%2==0, x\2, 3*x+1);
a375093(upto=600000) = {my(m=0); for (k=1, upto, np=issquare(k); j=k; while (j>1, j=nextc(j); if (issquare(j), np++)); if (np>m, m=np; print1(k, ", ")))}

Crossrefs

Cf. A000290, A006877, A008884, A078373.

Sequence in context: A146151 A306681 A254334 * A028855 A299597 A143014

Adjacent sequences: A375090 A375091 A375092 * A375094 A375095 A375096

Keyword

nonn,more

Author

Hugo Pfoertner, Jul 29 2024

Status

approved